Isothermal compressibility of hadronic matter formed in relativistic nuclear collisions

We present the first estimates of isothermal compressibility (\kT) of hadronic matter formed in relativistic nuclear collisions ($\sqrt{s_{\rm NN}} = 7.7$ GeV to 2.76~TeV) using experimentally observed quantities. \kT~is related to the fluctuation in particle multiplicity, temperature, and volume of the system formed in the collisions. Multiplicity fluctuations are obtained from the event-by-event distributions of charged particle multiplicities in narrow centrality bins. The dynamical components of the fluctuations are extracted by removing the contributions to the fluctuations from the number of participating nucleons. From the available experimental data, a constant value of \kT~has been observed as a function of collision energy. The results are compared with calculations from UrQMD, AMPT, and EPOS event generators, and estimations of \kT~are made for Pb-Pb collisions at the CERN Large Hadron Collider. A hadron resonance gas (HRG) model has been used to calculate \kT~as a function of collision energy. Our results show a decrease in \kT~at low collision energies to \sNN~$\sim$~20~GeV, beyond which the \kT~values remain almost constant.